A general formulation is considered for the free vibration of curved laminated composite beams (CLCBs) with alterable curvatures and diverse boundary restraints. In accordance with higher-order shear deformation theory (HSDT), an improved variational approach is introduced for the numerical modeling. Besides, the multi-segment partitioning strategy is exploited for the derivation of motion equations, where the CLCBs are separated into several segments. Penalty parameters are considered to handle the arbitrary boundary conditions. The admissible functions of each separated beam segment are expanded in terms of Jacobi polynomials. The solutions are achieved through the variational approach. The proposed methodology can deal with arbitrary boundary restraints in a unified way by conveniently changing correlated parameters without interfering with the solution procedure.

A numerical model for the prediction of vibration behaviors of a laminated submarine structure consisting of spherical, cylindrical, and cone shells with multiple built-in annular plates is reported in this article. With the aid of the first-order shear deformation theory (FSDT) concerning plates and shells, the energy expressions of each substructure are derived. The displacement functions in the energy functionals are expanded by the employment of Legendre orthogonal polynomials and circumferential Fourier series. Then, the Rayleigh–Ritz procedure is performed to obtain the eigenfrequency and the corresponding eigenmode of the submarine model. The correctness of the structural model is examined by comparing the results with existing papers and the finite element method, and the maximum deviation is not more than 2.07%. Additionally, the influence of the plate’s thickness, position, inner diameter, as well as the laying angle on the intrinsic vibration characteristics of laminated submarine-like structure is determined. The results reveal that rational geometry design and assemblage benefit the vibration performance of the combination. Increasing the thickness of all the annular plates, decreasing the inner radius, and regulating the laminated scheme, make remarkable influence on structural free vibration, with the maximum relative changing rate of frequency exceeding 97%, 16%, and 23%, respectively.

This paper provides a numerical solution to the vibration of a rotating cross-ply laminated combined conical-cylindrical shell in the thermal environment. Its numerical discrete solution method uses the meshless method. The combined shell assumed the temperature independence of material property is divided to the fundamental conical and cylindrical shell substructures, and the theoretical formulation for each substructure is derived based on the first order shear deformation theory (FSDT) and Hamilton’s principle. The effects of the initial hoop tension and temperature change are considered through the kinetic energy reflecting the effects of centrifugal and Coriolis forces and additional strain energy by the nonlinear part of the Green–Lagrange strains. The substructures are then assembled according to the continuity conditions. The boundary and continuity conditions are simulated by introducing artificial virtual spring technology. The displacement component in the theoretical formulation is approximated using a meshless Chebyshev-RPIM shape function. The reliability of the method is verified by comparing with mature and reliable results. The free vibration characteristics of the rotating combined conical-cylindrical shell structure under various sizes, speeds and temperatures are given by numerical examples.